Optically trapped room temperature polariton condensate in an organic semiconductor

The strong nonlinearities of exciton-polariton condensates in lattices make them suitable candidates for neuromorphic computing and physical simulations of complex problems. So far, all room temperature polariton condensate lattices have been achieved by nanoimprinting microcavities, which by nature lacks the crucial tunability required for realistic reconfigurable simulators. Here, we report the observation of a quantised oscillating nonlinear quantum fluid in 1D and 2D potentials in an organic microcavity at room temperature, achieved by an on-the-fly fully tuneable optical approach. Remarkably, the condensate is delocalised from the excitation region by macroscopic distances, leading both to longer coherence and a threshold one order of magnitude lower than that with a conventional Gaussian excitation profile. We observe different mode selection behaviour compared to inorganic materials, which highlights the anomalous scaling of blueshift with pump intensity and the presence of sizeable energy-relaxation mechanisms. Our work is a major step towards a fully tuneable polariton simulator at room temperature.


Characterisation of 1D trapping for more pump separations
-c shows real-space images of the cavity above threshold excited by two pump spots separated by 5 μm, 6.6 μm, and 7.2 μm. By resolving the line between the centres of two pump spots, the energy distribution of polaritons in the 1D potential trap is shown in Fig. S2d-e. By controlling the separation between the pump spots, the shape of the 1D potential is directly modified, leading to different numbers of quantum states trapped inside the potential.
Apparently, for shorter separations, fewer condensate states can be observed with polaritons occupying lower energy states, whereas for longer separations, more quantised states are resolved, and polaritons favour the higher energy states at just above threshold. Figure S3. Characterisation of one-dimensional trapping with more different separations. a-c, Real-space images of condensate emission for two 6.6 μm × 4.5 μm pump spots separated by 5 μm (a), 6.6 μm (b), and 7.2 μm (c). d-f, Corresponding real-space spectra along the centre of real-space images indicated by dashed line in (a).

Power dependence of quantised states in 1D trap
While the energy spacing of quantised states shows an inverse dependence on the pump separation, increasing the pump power of the two pump spots while keeping the separation constant only slightly increases the energy spacing (Fig. S4).

Theoretical calculations for power dependence of polariton populations
We assume driving of the polariton condensate to have the same spatial profile ( ) as the pump spots, disregarding the small diffusion of initially excited hot excitons. The reservoir contains many modes at different frequencies below the external drive frequency, and through intractable dynamics, excitons will redistribute among those and partially thermalise. 1 Ultimately, this leads to a large occupation of a low-energy polariton mode, where condensation will take place. For the case of multimode polariton condensation as studied in this work, it can be expected that lower energy modes experience a higher driving in the GPE framework. Assuming driving strength that decreases linearly with frequency up to a cut-off , this gives a driving contribution 2 In addition, we consider uniform incoherent losses through the mirrors at rate . Finally, we note that steady-state occupations above threshold are reached because of saturation of the exciton reservoir. Its effect can be included in the GPE by an incoherent nonlinearity ( ) (''nonlinear loss'') with the same spatial dependence as ( ), and height 0 .
Putting everything together, we obtain the driven-dissipative GPE The frequency-dependent driving equation (S1), naively, seems to suggest relatively higher driving of lower energy modes and thus a mode occupation that decreases monotonically with these energies. However, it is also important to consider a complementary mechanism: the overlap of the mode with the pump spot which will in general be higher for modes of higher . Indeed, Askitopoulos et al. have reported that in a circular trap in a GaAs microcavity, this effect alone has led to a maximal occupation that always takes place at the mode of highest that fits in the trap. 3 The relative intensities of the different modes are thus determined by an interplay of these two mechanisms. Although the frequency-dependent driving equation (S1) is known to be present already in inorganic polaritons, 1,2 we might expect it to be more pronounced in organic polariton experiments that operate at room temperature 4 and as such more susceptible to fluctuations from the environment, hence the different end result with respect to that reported in GaAs microcavity. 3 To perform these dynamical simulations, we also note that equation (S2) disregards spontaneous emissions in the condensate and the fluctuations they induce. This is typically justified for large occupations when stimulated processes dominate. However, for the initial evolution from an empty cavity, this omission is troublesome, as stimulated processes are absent. One option would be to add noise to equation (S2) explicitly in some form, 5,6 however, the resulting stochastic differential equations are numerically more demanding. 7 Instead, we opt to add a small amount of noise to the initial vacuum state to break the symmetry.
The increase of the pump power leads to a higher occupation of the lower mode as shown in Fig. 3b, which cannot be explained by equation (S2) alone, as the gain saturation cannot be expected to lead to non-monotonic behaviour. Unlike in inorganic microcavities, the potential remains almost constant with 0 above threshold in the organic case. 8 We will consider three different hypotheses for the observed behaviour. First, we notice that the increasing drive does result in an overall blueshift of the modes that is experimentally observable in Fig. 3a and 3b. Denoting the height of the Gaussian pump profile by 0 , we might then envision a shift of the frequencies Δ( 0 ) to the bare mode frequencies such that + Δ( 0 (1) ) < Ω while + Δ( 0 (2) ) > Ω, for two different pump powers 0 (1) , 0 (2) , i.e., the blueshift brings the modes to frequencies that are no longer driven. However, it is clear from Fig. 3a and 3b that the experimentally observed blueshifts are definitely too low to account for the phenomenon. Assuming a global blueshift of 1 meV, which is certainly more than observed, and 0 = 20 , where is the polariton decay rate, this fails to reproduce Fig. 3b as shown in Fig. S5a.
Second, although true optical nonlinearity is known to be negligible ( = 0 as discussed above) for organic polaritons, effective mechanisms, such as quenching of the Rabi splitting, may mimic its effect 8 and result in the appearance of a finite contribution = (which would be in addition to quenching of Rabi splitting contributing to ( )). However, as observed in Fig. S5b with 0 = 20 and a large optical nonlinearity of = 100 meV • μm added, this situation does not occur; instead the finite nonlinearity merely leads to an energy shift as discussed above and blurring of the energy levels.
Third, we consider the occurence of stimulated energy relaxation at rate , such as appearing from phonon scattering. [9][10][11] The significance of a stimulated mechanism would increase with 0 . To take this effect into account, a term is added to the right-hand side of equation (S2), where ( , ) is an effective chemical potential that ensures that the number of particles is conserved when they relax to lower modes. Figure 3d shows that this properly reproduces the shift in mode occupations with increasing pump power towards lower , as seen in the experiment. Figure S5c shows the calculation with 0 = 12 and = 10 μm/(meV • fs). We observe that because of the lower driving, it retrieves the linear result matching Fig. 3a, even if is fixed. Figure S6 shows the characterisation of the cavity excited by a small Gaussian laser beam   where the PL intensity transits from the sublinear to the superlinear regime in Fig. S8a. It is worth noting that the linewidth of PL spectra below threshold is broader than that excited by four pump spots, resulting from the interaction between polaritons and the overlapping exciton reservoir. When pumped above threshold, the linewidth dramatically reduces to 1.28

Single spot condensation
Supplementary Information 8 meV, which is 1.5 times that of the 2D trapped condensate and exhibits a slight broadening due to polariton-polariton and polariton-exciton interactions induced decoherence process. 17,18 The localised condensate shows a blueshift of 2.1 meV at 3 Pth (Fig. S8c).